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User blog:Granpa/Natural units
Fundamental units: *Time *Space *Mass *Charge Coulomb's law states that: : F=k_e\frac{q_1 q_2}{d^2}, where: * k_e is the Coulomb constant which is the "stiffness" of space. If the Coulomb constant is "negative pressure" then it has units of Force/area which gives: : F=\frac{F}{d^2} \frac{q_1 q_2}{d^2}, Therefore: : q=d^2, Charge is therefore no longer a fundamental unit but instead has units of distance squared. Natural units In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of speed. In Lorentz–Heaviside units (rationalized units), Coulomb's law is: * F=\frac{q_1 q_2}{r^2} \frac{1}{4 \pi}, In Gaussian units (non-rationalized units), Coulomb's law is: * F=\frac{q_1 q_2}{r^2}, Planck units are defined by : = ''k = 1}}, Stoney units are defined by: : = e'' = ''k = 1}}, Hartree atomic units are defined by: : = ''ħ = k'' = ''k = 1}} : }} Rydberg atomic units are defined by: : }} = 2''m'' = ħ'' = ''k = k'' = 1}} : }} Quantum chromodynamics (QCD) units are defined by: : = ''ħ = k'' = 1}} 'Natural units' generally means: : = 1}}. where: * is the speed of light, * is the reduced Planck constant, * is the gravitational constant, * }} is the Coulomb constant, * is the Boltzmann constant * is the elementary charge, Summary table where: * is the dimensionless fine-structure constant * }} is the dimensionless gravitational coupling constant * is dimensionless proton-to-electron mass ratio Fine-structure constant The Fine-structure constant, , in terms of other fundamental physical constants: : \alpha = \frac{1}{4 \pi \varepsilon_0} \frac{e^2}{\hbar c} = \frac{\mu_0}{4 \pi} \frac{e^2 c}{\hbar} = \frac{k_\text{e} e^2}{\hbar c} = \frac{c \mu_0}{2 R_\text{K}} = \frac{e^2}{4 \pi}\frac{Z_0}{\hbar} where: * is the elementary charge * is the mathematical constant pi * is the reduced Planck constant * is the speed of light in vacuum * is the electric constant or permittivity of free space * is the magnetic constant or permeability of free space * is the Coulomb constant * is the von Klitzing constant * is the vacuum impedance or impedance of free space Gravitational coupling constant The Gravitational coupling constant, , is typically defined in terms of the gravitational attraction between two electrons. More precisely, : \alpha_\mathrm{G} = \frac{G m_\mathrm{e}^2}{\hbar c} = \left( \frac{m_\mathrm{e}}{m_\mathrm{P}} \right)^2 \approx 1.751751596 \times 10^{-45} where: * is the gravitational constant * is the electron rest mass * is the speed of light in vacuum * is the reduced Planck constant * is the Planck mass Boltzmann constant The Boltzmann constant, , is a scaling factor between macroscopic (thermodynamic temperature) and microscopic (thermal energy) physics. Macroscopically, the ideal gas law states: : p V = N k_B T = N k_B m v^2 = N k_B 2 E, where: * is the pressure * is the volume * is the number of molecules of gas. * is the Boltzmann constant * is the temperature * is the velocity **Twice the velocity means twice as much momentum transferred per collision and twice as many collisions per unit time. * is the kinetic energy per particle Therefore temperature is twice the energy per degree of freedom per particle * T = 2 E Electromagnetism Gravitoelectromagnetism According to general relativity, the gravitational field produced by a rotating object (or any rotating mass–energy) can, in a particular limiting case, be described by equations that have the same form as in classical electromagnetism. Starting from the basic equation of general relativity, the Einstein field equation, and assuming a weak gravitational field or reasonably flat spacetime, the gravitational analogs to Maxwell's equations for electromagnetism, called the "GEM equations", can be derived. GEM equations compared to Maxwell's equations in SI units are: where: * E'g is the static gravitational field (conventional gravity, also called ''gravitoelectric in analogous usage) in m⋅s−2; * '''E is the electric field; * B'''g is the gravitomagnetic field in s−1; * '''B is the magnetic field; * ρ''g is mass density in kg⋅m−3; * ''ρ is charge density: * J'g is mass current density or mass flux ('J'g = ''ρ''g'vρ, where v'''ρ is the velocity of the mass flow generating the gravitomagnetic field) in kg⋅m−2⋅s−1; * '''J is electric current density; * G'' is the gravitational constant in m3⋅kg−1⋅s−2; * ''ε''0 is the vacuum permittivity; * ''c is the speed of propagation of gravity (which is equal to the speed of light according to general relativity) in m⋅s−1. CGS References Category:Blog posts